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    Investigation of optical soliton solutions of higher-order nonlinear Schrödinger equation having Kudryashov nonlinear refractive index
    (Elsevier GmbH, 2023) Ozisik, Muslum; Secer, Aydin; Bayram, Mustafa; Cinar, Melih; Ozdemir, Neslihan; Esen, Handenur; Onder, Ismail
    Purpose: In this paper, optical solitons of higher-order nonlinear Schrödinger equation with Kudryashov's sextic power-law of nonlinear refractive index are investigated via the direct mapping method. The considered model identifies the optical soliton pulse propagation in the optical fibers. Deriving the optical solutions of investigated model such as sextic power is critical but difficult work. The primary aim of this paper is to graphically examine the impact of power-law nonlinearity (pLawNL) and chromatic dispersion (CD) parameters clarifying self-phase modulation (SPM) in the equation on soliton behavior as well as obtaining optical soliton solutions. Methodology: To according to the used technique, we first used the complex wave transform to generate the nonlinear ordinary differential equation (NLODE) form of the nonlinear Schrödinger equation (NLSE) with Kudryashov's sextic power-law the nonlinear refractive index (SPLawNRI). Then, we were able to produce a system of linear equations in polynomial form by using the approach. Different solution sets including the values of the parameters of the studied equation and the suggested approach were produced by solving the linear system of equations. Findings: We acquired the optical soliton solutions of the main equation after inserting the sets and wave transformation into the solution functions suggested by the approach. The constraint conditions for the related solutions were suggested. We proved that the gained solutions satisfied the NLSE with Kudryashov's SPLawNRI under the suggested constraint conditions. Originality: We present contour, 3D and 2D depictions in various simulations in figures to comment the obtained solution functions. Besides, we investigate the effects of the power-law nonlinearity parameter that expresses SPM in the main equation and the parameter that are the group velocity dispersion (GVD) or chromatic dispersion (CD) on soliton behavior. The results suggest that the utilized approach is efficient, reliable, and powerful to be readily applied to various NLSEs with higher-order or higher pLawNLs that characterize real-life problems. © 2023 Elsevier GmbH
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    Investigation of soliton solutions to the Peyrard-Bishop-Deoxyribo-Nucleic-Acid dynamic model with beta-derivative
    (World Scientific Publ Co Pte Ltd, 2024) Secer, Aydin; Ozisik, Muslum; Bayram, Mustafa; Ozdemir, Neslihan; Cinar, Melih
    This study purposes to extract some fractional analytical solutions of the Peyrard-Bishop-Deoxyribo-Nucleic-Acid (beta-PBDNA) dynamic model with the beta-derivative by the unified Riccati equation expansion method (UREEM). Furthermore, we examine the role of various parameters of the fractional model on the soliton dynamic. The research focuses on computational biophysics and materials science, examining the impact of various parameters on the fractional model. This paper contributes to understanding soliton solutions and the beta-PBDNA dynamic model, demonstrating the applicability of the UREEM method to various fractional models. Some soliton solutions of the model are successfully generated by applying the UREEM. Implementing the UREEM, we take a fractional wave transformation to convert the model into a nonlinear ordinary differential equation. So, a linear equation system is generated. After the system is solved, the soliton solutions are gained for the appropriate solution sets. Finally, 3D, 2D and contour graphs of diverse solutions are depicted at suitable values of parameters. In addition, this paper presents 3D, 2D and contour graphs of various solutions with suitable parameter values. The results are beneficial for interpreting the model in future work and confirm that UREEM is effectively applicable to diverse fractional models, coupled with a comprehensive graphical analysis of how different parameters influence these solutions.
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    Nonlinear complex generalized zakharov dynamical system inconformal sense utilizing new kudryashov method
    (Iop Publishing Ltd, 2024) Secer, Aydin; Bayram, Mustafa; Ozdemir, Neslihan; Onder, Ismail; Esen, Handenur; Cinar, Melih; Aydin, Huseyin
    We take into account the nonlinear complex generalized Zakharov dynamical system which models the spread of the Langmuir waves in ionized plasma, in the conformal sense in this manuscript. Fractional wave transformation is enforced to convert the nonlinear fractional system to a nonlinear ordinary differential equation system. The new Kudryashov method which was recently introduced and is an efficient method, is implemented to the presented equation to acquire analytical solutions. The required constraint conditions are offered to ensure the validity of the obtained solutions. To analyze the physical interpretations for some of the produced solutions, we illustrate some graphical representations. We derive the bright and singular solitons. Furthermore, 2D views of the behavior of the solitons are represented to investigate the effect of the values of the parameters in the proposed model and fractional parameters. Also, the modulation instability of the model is investigated to ensure the obtained results are stable.